Strange Particle Production

Fortschritte der Physik 11, 479-501 (1963)

Strange Particle Production

V. S. BARASHENKOV and J. PATERA

Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Dubna

A great of papers is devoted to the investigation of the processes of the strange particle production. However, a major part of the results obtained is insufficiently accurate and may be considered as a rough preliminary estimate only. Further we shall consider in detail the part of the experimental information which concerns the cross sections for the strange particle production. At present the cross sections for the hyperon production in pion- nucleon collisions a t an energy T < 1,5 BeVl) and the relative probabilities of the K-meson pair production by the antinucleon annihilation are known most precisley. In other cases still few direct measurements of the cross sections have been made, and the conclusions about the magnitude of these cross sections can be drawn only on the basis of indirect data. In what follows we shall use the following abbreviated notations for the methods by which the experimental data have been obtained:

H-BC and P-BC the hydrogen and propan bubble chambers respectively ; H-DC and D-DC the hydrogen and deuterium diffusion chambers; C counters ; Em H-Em particles produced in irradiating the hydrogen target are

N

In cases when in determining the cross sections one has essentially used theoretical assumptions, these will be given in the corresponding remarks. We shall aduce the same errors as indicated in the experimental papers. If the cross sections are determined from indirect data, the given errors can characterize only the accuracy of the experimental data used. The true errors of the cross sections in these cases are noticeably larger than the indicated ones but of the same order of magnitude. When the errors due to the recalculation are essentially larger than the experimental ones, one will indicate only the order of the cross section magnitude.

the interaction of primary particles in the photoemulsion ;

detected in the photoemulsion. method of measurement is not indicated.

1. Two particle Reactions

To check the derivations of theoretical models describing the strange particle production one uses the cross sections for two-particle reactions with strange

I) Here and in the following T is the kinetic energy of particles in lab. system.

480 V. S. BAEASHENKOV arid J. PATERA

mesons and hyperons. I n doing so, one noticeably simplify the theoretical calcu- la tions. The available experimental cross sections for such reactions are given in the tables 1-5. These tables contain also the relative probabilities

where the total cross section for inelastic reactions bin & Gain is obtained by interpolating the available experimental data [l]. The values of the threshold energy Tth are given in the tables. For the sake of illustration basic experimental data are plotted in Figs. 1-2. When for the same energy T we have N independent measurements made by

T a b l e I The cross section for the reaction x- + p -+A + KO

~~

T [ BeV]

Ttl, := 0.74 0.775 0.793 0.8 0.81 0.829 0.871 0.88 0.90 0.91 0.95 0.96 0.96 0.96 0.99 0.99 1.01 1.1 1.1 1.1 1.1 1.2 1.3 1.46 4.85

15.86 63.86

- H-BC [2] H-BC [Z ]

H-BC [ Z ] H-BC [ Z ] H-BC [ 2 ]

H-BC [ a ] P-BC [7] P-BC [a] H-BC [ 7 ] H-BC [4] H-BC [B] H-BC [3] H-BC [lo]

P-BC [ 3 ] P-BC [3]

H-C [3]

H-BC [GI

H-BC [4]

H-BC 141 P-BC ~ I I I P-BC P-BC [ 7 ] H-BC [I21

H-BC [14]2) H-HC [I31 ')

H-BC j-iq)

0 0.056 & 0.015 0.14 & 0.02 0.09 0.03 0.37 & 0.03 0.43 f 0.04 0.56 + 0.04 0.95 & 0.1 1.20 & 0.07

0.58 & 0.12 0.82 i 0.13 0.90 & 0.07

0.65 + 0.10

0.69 5 0.12

0.58 & 0.12

0.49 * 0.11 0.68 0.03 0.27 5 0.04 0.26 & 0.04 0.52 * 0.02 0 22 It 0.06

0.32 & 0.06 0.238 & 0.041 5 0.12 < 0.34 0.05 c 0.39 $- 0.07

0.29 5 0.05

0 0.3 f 0.1

0.6 & 0.2 2.3 & 0.3 2.4 0.3 2.9 $- 0.4 4.7 f 0.9

0.9 & 0.2

6.0 & 1.0 3.0 & 0.8 3.0 & 0.8 4.0 & 0.8 4.3 & 0.9 2.8 & 0.8 4.1 & 0.9 2.3 & 0.8

1.5 & 0.4 1.4 f 0.4 3.1 & 0.7 1.2 1 0 . 4 1.8 & 0.5 1 . G + 0.4 1.2 0.3 5 0.F

< 1.5 & 0.4

3.2 * 0.6

1.7 3: 0.5

2) The indicated value is the eiimmary cross section for thc reaction x-+ p -+ A + KO 4- nr, whore n = 0, 1, 2 . . . This value is obtained under the assumption that 0 ~ ~ g - t nx - U C ~ K ~ + l zx .

Strange Particle Production 481

T [BeV]

Ttl, = 0.86 0.95 0.96 0.96 0.96 0.99 0.99 0.99 1.09 1.1 1.1 1.2 1 .:3 1.46 4.85

15.86 23.86

Table 2

The cross section for the reaction X- + p -+ C" + KO

- H-BC 131 H-BC [7] H-BC [ 4 ] H-RC [9] H-DC [3] H-BC [ lo] H-BC [ a ] H-BC [I51 P-BC [3] P-BC [ I l l P-BC [7] P-BC [ 7 ] H-BC [I21 H-BC [13l3)

H-BC [1413) H-BC ~2413)

0 0.36 5 0.09 0.25 0.10 0.34 5 0.07 0.35 f 0.09 0.41 0.07 0.19 0.04 0.34 f 0.04 0.39 f 0.04 0.16 f 0.04

0.12 & 0.04 0.24 f 0.06

0.21 & 0.06

0.106 f 0.021 5 0.12

<0.38 * 0.7 (0.34 rf: 0.5

-~ ~~ ~ ~

0 1.7 0.7 1.2 f 0.6 1.6 4 0.5 1.7 -& 0.7 2.0 f 0.6 0.9 & 0.3 1.6 rf: 0.4 2.2 & 0.6 0.9 f 0.4 1.2 -& 0.6 0.8 0.4 1.2 & 0.5 0.5 -& 0.2 - < 0.5

(1.5 -J= 0.4 <1 .7 & 0.5

Fig. 1. TIIF cross section for the reaction x- + p -+A + K" (in onits cm2)

3) The indicated value is the summary cross section for the reaction TI- + P -+ A" + K" + U X ,

where = 0,1,2, . . This value is obtained under the assumption that b ~ o r + l l S i - u A x i + fin.

482 V. S. BARASHENKOV and J. PATERA

different authors we give in these figures the mean values:

I fr-+~-zO+K' I

U15

1

Pig. 2. The cross sections fur the C-hyperon production in two-particle reactions (in units ram2)

The resonance behaviour of the cross section for the A + KO pair production near T N 0,9BeV attracts attention. At the resonance point the section GAKO increases by a factor of 4-6. The width of the resonance peak is about 50-100 MeV.


Table 3 The Cross section for the reactions x- + p --f C- + K+

T [BeV]

Tth = 0.86

0.88

0.89 0.90 0.92 0.93 0.94 0.95 0.95 0.96 0.96 0.96 0.97 0.98 0.99 0.99 0.99 1 1.01 1.02 1.04 1.05 1.06 1.09 1.09 1.09 1.1 1.2 1.3 1.46 4.85

15.86

-

H-BC [I61

H-BC [I61 H-BC [IS] H-BC [I61 H-BC [ I S ] H-BC [I61 H-BC [I61

€1-BC [7] H-BC [7] H-BC [5] H-BC [ I S ] H-BC [IS]

H-BC [ S ]

H-DC [3] H-BC [I01 H-BC [I61 H-BC [I61 H-BC [ IS] H-BC [IS] H-BC 1161 H-BC [I61 H-BC [I61 H-BC [I51 D-DC [I71 D-DC [I7]*) P-BC [ I l l P-BC [7] P-BC [7] H-BC [I21 H-BC [1335) H-BC [ I4 ] ' )

(JC-K+ cmz]

0 + 0.03

0.16 & 0.05 0.16 & 0.05 0.10 f 0.04 0.16 & 0.05 0.23 f 0.06 0.14 & 0.05 0.09 5 0.04 0.25 5 0.07 0.24 & 0.06 0.09 & 0.04 0.23 5 0.05 0.17 & 0.05 0.22 & 0.03 0.22 f 0.03 0.25 & 0.07 0.21 f 0.08 0.31 & 0.07 0.29 & 0.07 0.26 & 0.07 0.25 f 0.07 0.25 5 0.07 0.27 i 0.03 0.200 & 0.028 0.177 & 0.033 0.17 f 0.04 0.13 f 0.03 0.23 & 0.04 0.238 & 0.029 < 0.05 < 0.29 & 0.04

0.05 - 0.02

0

0.3 f 0.1

0.8 & 0.3 0.8 5 0.3 0.5 & 0.3 0.8 & 0.3 1.1 & 0.4 0.7 f 0.3 0.4 & 0.2 1.2 f 0.5 1.1 & 0.4 0.4 & 0.2 1.1 i 0.4 0.8 & 0.3 1.0 i 0.3 1.0 * 0.3 1.2 f 0.5 1.0 f 0.4 1.5 0.5 0.4 0.5 1.3 0.5 1.2 5 0.5 1.2 5 0.5 1.5 f 0.4 1.1 & 0.3 1.0 0.3 0.9 f 0.4 0.8 f 0.3 1.1 & 0.3 1.1 f 0.2 < 0.02

(1.3 5 0.3

An increase of the cross sections in the region T M 1 BeV is observed for the reactions with the Z-hyperon production, as well. However, this increase is less strong than for reactions with the A-hyperon production, perhaps it is of a purely kinematic origin: increase of the cross section near the threshold energy T = T t h and its decrease a t an energy T > 1 + 1.5 BeV which is due to a rapid increase of the number of possible channels in a inelastic reaction. (We recall that the cross section oin a t T 2 1 BeV changes very little, see [ l ] ) . The latter explains the decrease of the cross sections of all the two-particle reactions at an energy T > 1 BeV.

4) Obtained from the condition of the isotopic spin invariance. 5) The indicated value is the summary cross section for the reaction x- + p 3 2- + K+ + nx where n = 0, 1, 2 . . . This value is obrained under the assumption that UX-K+ nx N U X - K ~ + ~ ~ .


T [BeV]

Ttl, = 0.86

0.91

0.91 0.98 0.99

0.99

1

1 1.03 1.09 1.09 1.09 1.1 1.26 4.85

15.86

T a b l e 4 The cross section for the reaction n+ + p -+ C+ 4- K+

Method

-

H-BC [ I S ] H-BC [I91 H-BC [ZS] H-BC [ZOl H-BC [el] H-BC [*?I P-BC [22] H-BC [ Z a ] H-BC [I81 1)-DC [17) D-DC [1;116) P-BC [U] H-BC [I81 H-BC [1SJ7) H-BC ~1417)

0 + 0.018

0.067 0.005 0.088 f 0.026

0.033 - 0.012

0.19 + 0.09 - 0.07

O'lG + 0.08 - 0.06

0.41 & 0.21 0.08 0.205 0.014 0.25 0.02 0.171 5 0.031 0.185 & 0.035 0.15 & 0.05 0.42 0.07 < 0.05

(0.36 0.06

0

0.3 & 0.2

0.6 0.2 0.6 f 0.2 1.4 5 0.7

1.1 * 0.6

2.9 * 1.6

0.6 1.0 * 0.2 1.6 & 0.3 1.1 0.3 1.2 3 0.4 0.9 & 0.4 1.8 f 0.5 < 0.2

<1.6 & 0.5

Near the threshold T w Ttl, the experimental cross sections for the two-particle reactions are well approximated b y the function [87]

a ( T ) = a ( T - Tt)'/z where

(3)

a = (0.045 5 0.004) .

h = (0.038 & 0.002) . m = (0.0082 & 0.0006) . iO-Z7 cm2 MeV-'I2 for reaction z+ + p -+ C+ + K+.

em2 MeV-'/- for reaction x- + p + C" + KO

om2 MeV-'IA for reaction z- + p -+ Z- + K+

At T > i BeV direct measurements of the cross sections for the two-particle [ 4 ] reactions are not carried out yet. As an extreme upper estimate of these cross sections we can use the experimentel data on the cross sections for reactions with the production of strange particle pairs A + K and 2 + K accompanied by a different number of x-mcsons. (Sec remark to the tables 1-4). It should be expected that the cross sections for the two-particle reactions are considerably smaller than such summary cross sections. (This is confirmed also by calculations of the relative magnitude of the cross sections for different channels using the statistical theory of multiple production of particles).

6 ) Obtained from the rondition of the isotopic spin invariance. 7 ) The indicated values are the summary cross section for the reaction X+ + p -+ C+ + K+ + 4- nx where n = 0, 1, 2.. . under the assumption that u ~ + K + + ~ ~ - U C + K ~ + ? , ~ .


T a b l e 5 The cross sections for the two-particle antinucleon annihilation + p --t X + Y

T [BeV]

0.92 0.92 0.92 1.26 1.29

1.29

2.25 2.25 2.25 2.5 2.5 2.5 2.5 2.55

(2.25+2.85) 2.65

(2.25+2.86) 2.85 2.85

Method

H-BC [ 2 4 H-BC [24] H-BC [2i, 251 H-BC [Z5] H-BC [25]

H-BC [25]

H-BC [26] H-BC [ZS] H-BC [27] H-BC [Z?'] H-BC [Z7] H-BC re71 H-RC [27]

H-BC [ZS]

H-BC [ZS]

H-BC [26] H-BC [26]

~7 cmz]

55 & 18

57 1 18 55 f 40 40

40

38 * 7 8 1 3 4 & 2.5

94 & 20 - 30 -20 - 15

78.5 & 23

91 &25

46 f 12

< 50

7 f 3.5

0.09 -+ 0.04

0.10 f 0.04 0.10 & 0.08 0.08

0.08

(0.1

0.085 1 0.025 0.018 f 0.009 0.089 f 0.07 0.21 1 0.06 -0.067 -0.045 -0.033

0.17 & 0.07

0.2 & 0.008

0.1 & 0.04 0.015 & 0.009

- The threshold energy for production of hyperons pairs A + x, h + C, 2 + C and 2 + 8 is 0.745, 0.94, 1.13 and 1.83 BeV., respectively. For the production of a K-meson pair Tth = 0.

2. The K-Meson Pair Production

Besides the two-particle reactions of great interest are the reactions with the K-meson pair production since the mechanism of production of such pairs may differ from the mechanism of the strange particle production in reactions with hyperons8). Besides, a separate investigation of reactions with K-meson pairs and reaction with the hyperon production is very important for choosing parameters in the statistical theory of multiple production of particles [28,29]. However, if we do not take into consideration the antinucleon annihilation, where at energies not exceeding several BeV the hyperon production probability is very small and the cross section for the K-meson pair production CTKK coincides with the total cross section for the strange particle production, the direct measurements of c~~ occur rarely. In most cases we can obtain only estimates based on more or less justified assumptions.

*) In the antinucleon annihilation a K-meson pair can be produced in two particle reaction. However, the cross section for this reaction is very small (see Table 5) since in most cases K-mesins are produced accompanied by several x-mesons.

33 Zeitschrift ,,Fortschritte der Physik", Heft LO

486 V. 8. BARASHENKOV and J. PATERA

The available values of CJKK abtained on the basis of direct and indirect experimental data are collected in the Table 6. Some of the values of OKK given in this table are determined from experimental data on the K--meson yield in the berylium and aluminium targets. Since in the

Interaction

P-P

P-n

N - N

- P-P

- P-n

ij-N

x--p

Z-N

Table 6 The cross section for K-meson pair production

T [BeV]

23

4 (1 +- 6)

( I -+ 6) 4

6 9

10 (20 f 30)

-0 -0 0.08

0.47 0.92 1.26

-0 0.47

0.14

(0 f 0.23)

(0 t 0.23)

1.46 1.85 4.7 4.85 6.65 9.86 15.7 15.86

4.3

Method

H-BC [ 241 ') lo)

P-BC [30] lo)

P-BC [3UI1O)

Em [31] 11)

Em[32] Em[33] P-BC [34]

P-BC [35]

H-RC [3G]

Em[32]

Em [38]

H-BC [36]

P-BC [35]

H-BC [I21 H-BC [39] lo)

H-DC [a01 lo)

H-BC [I31 P-BC [Pl] lo)

H-BC [86] H-BC [42]"') H-BC [la] lo)

[431

4.2 I 0.6 (0.2 & 0.1

0.15 & 0.07

5 0.3 -0.1 -0.3 -3

13)

13) 4.4 i 1.5

5.6 & 2.2 6 i l

7.4 & 2.1

la) 5.6 & 2.2

3.1 & 1.712)

-0.031 -0.1 -0.6 -0.7 1.6 & 0.4 2.0 0.3 2.21 & 0.25 2.3

5 0.8

13 & 2.5

(0.9 10.5

0.7 & 0.03

5 0.1 -0.3 -1 - 10 3$-1

4 + 1

s + 2 10.3 f. 1.1 13 $- 3

3 8 1 2

41-2

3.5 & 2.5

-0.15 -0.5 -2.5 -3 7.0 + 2.6 9.1 & 2.2 9.7 & 1

10

5 4

The threshold energy of the K-meson pair production is T = 2.47, 0 and 1.34 BeV for case N - N , F-N and x - N interactions rexpectively.

9) Obtained under the assumption that U A I ~ + + ~ ~ K + N O A K ~ + C " K ~ . 10) It was assumed that the different charge states of a K-meson pair have equal probility. 11) Estimate obtained from the average numbers of K--mesons produced. 12) Under the condition that oin(FN) 21 Oin(5P). '3) The cross section oin(ZN) a t T - 0 is unknown.


region of accelerating energies the probability of a simultaneous production of several pairs of K-mesons is extremely small then the average number of K--

(4) mesons produced is

GKK- nx- = 2 (1LK-)i wi = - i bin

Table 7 The ratio of the average numbers of K--andx- mesons produced in collision of protons withnuclei

p is the momentum of produced particles, 0 is the angle a t which these particles are emitted in the direction of the primary proton beam; Lab. sys.

T [BeV]

6 6 6 6

10 10

20 20 20 20 20 20

24 24 24 24

30 30 30 30 30 30 30 30 30 30 30 30 30

~ 30 30 30 30 30 30 30

33 33

33*

Nucleus

Polyethelen [4G] Be [46] Be [46] Be [46]

Be [47] Be [47]

Be [47] Be [47] Be [47] Be [47] Be [47] Be [47]

A1 [45--50] A1 [48-501 A1 [48-50] A1 [48-501

Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] A1 [47] A1 [47] A1 [47] A1 [47] 81 [47 ] A1 [47] A1 [47) A1 [47] A1 [47] A1 [47] A1 [47] ~i [a71

A1 [52] A1 [52]

0 [degrees]

0 0 0 0

9 9

4.75 4.75 4.75 9 9 9

6 6 6

16

4.75 9 9 9 9 9 9 9 4.75 4.75 4,75 4.75 4.75 4.75 4.75 4.75 4,75 9

13 13

13.25 13.25

~~ ~ ~

1.12 1.7 2 2.8

3 5.9

8.1 8.8

10.5 3 5.9 8.9

5 6 8 2

11.7 3 3.9 4.9 5.9 8 1.25 2.5 5.4 6.4 7.5 8.8

10.7 11.3 12.3 14.3 16.3 10 6 9

2 2.5

0.007 0.02 0.014 0.014

0.037 & 0.011 0.0069 f 0.0020

0.031 5 0.003 0.028 & 0.002 0.018 & 0.002 0.067 5 0.013 0.042 5 0.005 0.024 & 0.004

0.066 & 0.020 0.054 f 0.007 0.039 & 0.007 0.12

0.040 & 0.005 0.074 & 0.019 0.055 f 0.006 0.079 5 0.008 0.069 & 00.07 0.074 & 0.006 0.012 0.005 0.088 5 0.009 0.036 h 0.004 0.057 f 0.015 0.059 5 0.007 0.051 & 0.004 0.050 & 0.003 0.050 & 0.006 0.043 & 0.004 0.034 & 0.006 0.024 & 0.008 0.079 0.017 0.062 & 0.010 0.048 f 0.010

(8.9 5 1.3) * (8.5 5 1.3). lo-'


where Wi - is the probability of the i-th channel of an inelastic reaction. Hence, the cross section of the K-meson pair production is

In this case we took into account that for high energies, strange particles are produced accompanied by several x-mesons therefore the different charge states of the pair K+K have approximately equal probability and OICK rn ~ o K K - .

T /

3 Fig. 3. The cross section for the strange partirle production in inelastic N - N interactions (in units cma). The

marks arid 0 denots the values of oat and GKK respectively

/I Fig. 4. Thc strange particle production probability ost/oin c U K K / U ~ in inelastic 3 - N interaction ’

The experimental ratios of the numbers of produced K--and n--mesons are given in the Table 7 . These ratios change little in the transition from Be to Al. This points out that the experimental data of the table 7 characterize the primary p-N interaction rather than the subsequent internuclear interactions. (In the transition from nucleus Be9 to nucleus A127 the number of internuclear collisions is doubled approximately [44, 451). On the average, in the region of values of


p and 0 indicated in the Table 7 the quantity nK-/nx 5 0,Ol a t T = 6 BeV and of the order of 0.01 and 0.05 a t T = 10 and (20 - 30) BeV. However, the calculations made by means of the statistical theory of multiple production of particles have shown that in the considered region of p and 8 the momentum and angular distributions of x-- and K--mesons considerably are differ out. The data of the table 7 lead therefore to an overestimated value of the ratio of the average numbers E K - / Z x - and can give a concept of the magnitude of the order of a K K

only; more exactly

Thus obtained cross sections a K K agree with other data given in the Table 6.

Pig. 5. The strange particle production cross section in inelastic n-N iiltcractions. Notations are the same as in Fig. 3

For the sake of illustration the basic experimental data are plotted in Figs. 3-5 (in a number of cases the averaged values of the cross sections (2) are indicated).

3. Cross Sections for the Cascade =-Hyperon Production ,

The cascade hyperon production has been observed in many papers, however, the number of registrated events was very small in most cases. Therefore, the cross sections a= were estimated a t several points only(see Table 8 and Fig. 6). A part of the estimates was obtained fromtheanalysisof interactions withnuclei. Of course the obtained values should be considered as roughly tentative. The errors of ~ C T ~ indicated for these cases only statistics of events. I n the region of energies available to be investigated on accelerators the cross section for the Z-hyperon production, in any case for x - N interactions increases very rapidly. This is due to a large degree to it high threshold energy Tth.


A relatively large value of the cross section IS= in K-N interaction attracts attention. The hyperon production turns out to be in this case considerably more probable than in x - N interactions.

Tab le 8 The cross soction for E-hyperons production

Interaction l4)

P-P(Z-) P-P (S-) x--P (E-) x--P (E-) n-.P(&-) x--P (E-) x--N(E-)

x--N (Z-)

x--N (E-)

-

K--P (6-) K--N (3-) K--P (3.") K--P (8-)

T [BeV]

23 2.25 4.85 9.86

15.7 15.86 5.35

6.65

7.85

0.76 0.76 0.76 1.8

Method

H-BC 1143 H-BC [26] H-BC [I31 H-BC [86] H-BC [42] H-BC [ l a ] P-BC [5e]l5)

P-RC [53] 15)

P-BC [53]15)

P-BC [51] P-BC [55] P-BC [51] H-BC [SSJ

us omz] ~~ ~~ ~

i 50

- 6 4 2.5

14.3 f 4.8 5 20 < 60 + 3.1

+ 2.5

+ 4.4

- 2.3 - 1.6

- 3.6 - 2.1

-10.6 - 3.2 2 14

N 24 18 & 5

21.8 & 20

< 0.2

-0.03 0.008 & 0.005

0.068 f 0.03 Y (0.1 < 0.3

+ 0.014 No.o1 - 0.003

jO .08 & 0.01 0.1 * 0.05

-0.14 f 0.02 0.14 0.16

The threshold energy of the E-hyperon production T t h = 3.71 ; 2.19; 0.654 for case of N - N , x - N , K - N interactions respectively.

4 Fig. 6 . The cross section for the =--hyperon prodnetion in x-N interactions (in units emP)

14) In brackets it is indicated what type of E-hyperon has been investigated in the given paper. 15) Rought estimate obtained from the analysis of interactions with Cia.

Strange Particle Production 49 1

4. The Antihyperon Generation

As to the antihyperon production in x - N and N - N interactions only single cases of such events are available and it is difficult to draw come qualitative conslusions about the cross sections. In the energy region not exceeding two or three tens of BeV. The cross section for the antihyperon production is apparently of the same order of magnitude as that for the antinucleon production or somewhat smaller and constitutes only a very small part of the total cross section for the strange particle production. In paper [56] for the x-hyperon production cross section in n-- + p interactions a t T = 7 BeV the following estimate is obtained:

This value is close to the estimate of the cross section ojii > em2 obtained a t the same laboratory [57]. Approximately the same value of ax is obtained in x--p interactions a t an energy T = 10 BeV [86] :

= (5.2 f 3.2) . em2 = (2.3 i 1.4)% Gin

(hydrogen bubble chamber). In paper [42] in analysing 60000 photos of interaction of 16 BeV x--mesons only one case of the A-hyperon production was found in the hydrogen bubble chamber. In this paper the upper estimate of the cross section for the A-hyperon production

C J ~ 5 2 - 10-29 em2 rn 0.08% oin is obtained. A close estimate of the cross section

C J ~ w 3 * lo-'' cm2 0.1 yo bin

is obtained for pp interactions a t T = 25 BeV [ l a ] . This is approximately by an order of magnitude smaller than the cross section for the antinucleon production a t this energy (see [58]). It is quite possible that a t very large energies T > 10 BeV the cross section for the antihyperon production will exceed considerably the cross section oz (for more details see [SS]). Recently one has obtained quantitative estimates of and oz in the antinucleon annihilation (see table 5 ) . At an energy T s 1 BeV this cross section amounts to about 1 % of the total cross section for the strange particle production and to about the same value of the antinucleon production cross section. A so small magnitude of GX and o~ is probably explained by the fact that the antinucleon energy is near the threshold energy for A- and %-production. At high energies, reactions in which antihyperons are produced with x- and K- meson become important. At present the only paper [%I is known in which the cross sections for such reactions are measured :

- + A + no, CT = (41 & 17) . em2

o = (3.5 f 2 ) . 10-30 cm2 c= + X L + xo, P + P + {

a t T = 2.25 BeV.


P +

- A + N + K, o = (20 10). cmz

a t 21 = 2.55 BeV;

h + A + no, u m 40 . cm2

{- 2 h -+ Z+ + x0, G = (9.8 & 5) . 10-30 cm2 F + P +

a t T = 2.85 BeV. As we can see, these cross sections are of the same order of magnitude as those for the two-particle reactions in Table 6 . In paper [%I the E--hyperon production cross section have been first measured as well:

(see Table 8).

I - 1' + p --f G- + E-

5. The Total Cross Sections for the Strange Particle Production

The available experimental data on the total cross sections for strange particles are collected in Table 9. I n this table there are no data for the x+ - p interactions and for the antinucleon annihilation, as far as in the first case o,t m ax+K+ and this cross section is given in Table 4, and in the second one o,t m GKK and it is indicated in table 6. Of course, with increasing energy many other channels or the reaction will be realized with a noticeable probability, and the cross section oSt will noticeably exceed that indicated in tables 4 and 6. A considered part of the data of Table 9 are the estimates obtained on the basis of different asumptions. According to t'he character of the assumptions these estimates may be divided into three groups : 1. The estimates of the cross sections obtained by means of assumptions connecting the cross sections for the charged and neutral particle production. The higher the energy and the larger the number of produced particles the more exactly such assumptions are fulfilled. Estimates based on the assumptions connecting the cross sections for production of hyperon and K-meson pairs may be attributed to this points also. These assumptions are, generally speaking, fulfilled in definite energy intervals only and they should be considered (see footnotes to Table 9). 2 . The determination of the cross sections a,& from the analysis of interactions of particles with nuclei. In this way we can with good accurary determine the cross section Gst in case of the antinucleon annihilation at low energies. All the strange particles are produced in this case in the interaction wii>h one nucleon of the


T a b l e 9 The cross section for the strange particle production

H-BC [59] le)

H-DC [60] H-BC [61]17) HP [62-641 la)

H-DC [66] HP[65]

H-DC [66] C [67] Is) p is51 P [68] 20)

H-BC [l4lz1) C [67]19) P-BC [3OI22) CH(C'2) [69] P-BC [3OIz2) 24)

P [7O] 23)

24)

P [44, 7 2 I z 6 ) p ~311

24) CH(AlZ7) [72Iz2)

MCH (paraffin) [73Iz2)

Interaction

P-P P-P P-P P-P P-P P-P P-P P-P P-P P-P P-P P-n P-n N - N N - N N - N N-N W - N N - N N - N N - N *v- N

0.018 & 0.005 0.1 + 1.5

20.130 & 0.03 < 0.8 -0.3 -0.2 < 0.4 -0.08 & 0.12 2 3 2 1.3

7.3 & 0.7 -1.3 -0.5

' >0.09 rir 0.06 -0.6 -0.5 -0.5 -3

-3

-20

-10

N 1

N 10

I

T [BeV]

2 2.75 2.85 3 3 3 3 3 9 9

23 3 6 2.8 6 6 9 9 9

10 20 -+ 30

28

150 (10 f 100)

(50 + 250)

0.06 & 0.03 0.3 + 0.5

2 0 . 4 4 5 0.13 < 3 -1 -0.7 < 1.3 -0.25 5 0.3 2 10 2 4

23 & 5 -4 -2

-1.5 -2 -1.5 - 10 -3 - 10 - 30 - 60

- 30

>0.3 -J= 0.2

16) One gives the cross section for the reaction p + p + h + K + ; the cross section for the 3-hyperon production is considerably less. 17) The K-meson pair contribution is not taken into account. Obviously, this contribution is very small since the threshold of the K + pair production is by 0,s BeV less than the under consideration. 18) Estimate obtained from experimental data by means of the Fermi statistical theory. 19) Obtained under the assumption that ust - 2 (UA + ax.) and u K ~ Q ust. 20) Rough estimate obtained under the assumption that the cross section for production of Zo, C+, z'- and A-hyperons are approximately equal. The cross section for K-meson pair production is not taken into account. J 1 ) Besides assumptions indicated in the footnote to Table 6 is was assumed that cross sections for the charged and neutral hyperon production are approximately equal. 2 L ) In this case it was assumed that the cross sections for production of charged and neutral praticles are about equal. 2:J) Obtained from the analysis of interactions with the photoemulsion nuclei under the assumption that the K-meson pair production cross section are of the same order as the hyperon production cross section and the cross sections for charged and neutral hyperons production nre approximately equal. Apparently, the cross section ux measured in paper [70] is very under cstimated. L4) Rough estimate accorclings to the average numbers of the K+-mesOns produced. 2 5 ) Obtained from the analysis of interactions with the photoemulsion nuclei under the assumption that urt = %oKK+. Since in experiment one investigated only K+-mesons with energies I' 5 0.14 BeV then the remaining part of the cross section is added from the com- parison with the theoretical spectra calculated according to the Fermi statistical theory.


T a b l e 9 (continued)

Interaction

x--p x--p x--p n--p n--p "--p x--p x--p

x--p X--p x--I) x--p x--p x--p X--p x--p X--p x--p x--p X--p

x--p x--p x--p x--p x--p x--p

x N x N

K-1'

T [BeV]

0.775 0.793 0.8 0.929 0.871 0.91 0.95 0.90

0.96 0.96 0.99 0.99 0.99 1.1 1.1 1.2 1.3 1.46 1.85 1.9 4.7 4.85 6.65 9.86 15.86 16

1.5 4.3

1.8

Method

H-BC [%I H-BC [2] H-DC [3] H-BC [ 2 ] H-BC [%I P-BC [7Iz6)

H-DC and P [741

H-BC [8]

H-BC [ 7 ] H-BC [9] H-DC [3] H-BC [lo]

1'-BC [3IL7) H-BC [75]

11-BC [ 1 1 1 2 7 )

P-BC [7127) P-BC [7]"7, H-BC [ I%] H-BC [39] H-DC 1761

H-BC [I31

H-BC

H-DC [40]

P-BC [41]28)

H-BC [ l a ] H-XC [77 78Jz9)

D(CC721) C791 P [43]

H-BC [SSj30)

0.056 & 0.015 0.14 & 0.0'2 0.09 f 0.03 0.43 0.04 0.56 0.04

1.02 & 0.25 -0.9

0.8 + 1

1.32 & 0.18 1.02 * 0.2 1.48 & 0.13 0.90 * 0.12 0.9

- 0.8

>0.60 jI 0.07 >0.60 & 0.09 >0.54 & 0.07 >0.79 & 0.09

> 0.4 = l -1.2

0.924 & 0.095

1.14 3.2 5 0.6 3.3 f 0.4 3.6

-3

0.6 - 1.5

0.18 0.02

0.4 & 0.2

0.6 & 0.3 2.5 & 0.4 2.9 & 0.5

0.9 & 0.2

-4.5 4.9 * 1.9 3.8 + 6

6.3 & 1.8 4.9 1.7 7.0 & 1.6

4.3

- 3.8

4.3 * 1.2

>3.5 * 1.0 >3.5 & 1.1

4.4 f 0.9

>3.4 * 1.3 >4.0 & 0.9

> 1.9 21 4.8 -5

5 14.0 & 3.2 15.5 & 1.3 16 - 13

2.5 -6.6

1.2 & 0.4

nucleos. In subsequent interactions inside the nucleus occurs only the charge exchange of the strange particles produced and the change their momenta, Q C C U ~ .

Therefore

26) Estimate obtained under the condition uzo li UZ- = 0.16 (comp. table 3). 27) The cross section for the reactions with rr-mesons was not taken into account (the threshold energy of the rr-meson production Tx N 1 BeV). 28) In this case it was assumed that the production of the pairs of K-mesons with diEerent signs of the charge has equal probality and the cross sections for the charged and neutral hyperon production are about aqual. 2 9 Estimate obtained under the assumption that the cross section for the K-meson pair production is approximately equal to the doubted cross section for the hyperon production (comp. [ 4 2 ] ) . 30) In case of K-N interactions the strange particle cross section implies the cross section for reactions with the production of three or more strange particles, i. e. the cross section of production of an additional pair of strange particles.

Strange Partirle Production 495

At high energies measurements made on nuclei will give only the lower estimate ost since a part of strange particles will be produced in the annihilation of anti- nucleons already slowed down due to interactions inside the nucleus (we recall that the cross section ast(3'N) strongly depends on energy). The analysis of interactions with nuclei applied to the x - N and N - N interactions can give sufficiently presise values of the cross sections for the strange particle production if after the internuclear interactions the energy of particles does not exceed the threshold energy of the strange particle production. This is seen, e. g., from Table 10, where one gives the yield of strange particles (gst/oin) produced in the interaction of 1.5 BeV x--mesons with different nuclei (in accordance with the data of ref. [7'9]). The energy of most particles after the first x--N interaction is in this case insufficient for the production of strange particles. The quantity (cst/ain) in a wide interval from C1* to Pb208 proves to be practically independent of the atomic number of the target nucleus:

m 2.5%.

This agrees well wit,h the averaged quantity

calculated from experimental data of Tables 4 and 9, expecially as the yield of strange particles in ref. [79] is somewhat understated (strange particles were registrated according to their decays a part of decays being omitted according to the experimental conditions). At higher energy secondary x - N and N - N interactions in nucleus are of great importance. In this case we may obtain an estimate of the order of the quantity ast only. The cross section a s t ( N N ) is destorted by the secondary interactions especially strongly since a t an energy of several BeV ast ( N N ) . ost ( x N ) .

T a b l e 10 The yield of strange particles in the interaction of x--mesons and protons with nuclei (with

respect to the total cross section of alle inelastic reactions of nucleus) : ast/ojn yo X- + Nucleus 1 P + Nucleues T = 1.5BeV 1 T = 2.8BeV Targrt

ClZ 2.57 i. 0.36 0.333 0.118 0.246 & 0.085 0.668 5 0.161

Ft'6 1 2.25 i. 0.41 pb2W3 1 2.17 5 0.18

+ 28

I So in the interaction of 2.8 BeV protons with the carbon nuclei

For the nuclei of Pb this value is some what larger:

the strange particles are produced as a result of the internuclear x-N interaction [79]. yo. The yield of strange

particles strongly depends in this case on the substance of the target (see Table 10). 3. The estimates of the cross section ust according t o the yield of K+-mesons from the aluminium and berylium targets.

496 W. S. BARASHENKOV and J. PATERA

As at energies not exceeding severa.1 tens of BeV the probability of a simultaneous production of more than one K+-meson is not large, the cross section for reactions with K+-meson production

and, consequently,

(comp. formula (5)). The experimental values of the ratio (n,+/nn+) for different angles and momenta are given in Table 11. From this table it is seen that the ratio of average mumbers is about 0.02; 0.1; 0.2 for T = 6, 10 and 20 - 30 BeV respectively. In this case just as in calculating B K K the factor 1/3 should be taken into account (see formula (6)). From the above data i t is seen that with increasing energy the strange particle production cross section rapidly increases. If a t energies T w 1 BeV the cross sections o , t (xN) and o,t(&VN) amount to one percent only of the total cross section for all the inelastic channels, then a t T m (20 + 30) BeV this cross section increases by a factor of ten-twenty. The cross section increases especially rapidly in the antinucleon annihilation the yield of strange particles increases as much as three times in the energy interval A T m 1 BeV : If we extrapolate to a very high energy region the avaiable experimental data we may expect that a t energies of several tens of BeV and higher the cross section ust will practically coincide with the cross section bin and the strange particle production process will become predominant. From the experimental point of view this assumption can not be at present proved or disproved31). To this end a considerably more rich and pure experimetal information is needed. I n particular, the presence of a large number of hyperons in the core of atmospheric showers which are due to cosmic superhigh energy particles should lead to a number of charakteristic phenomena: to the difference of the energy spectra of the electron proton component in the dense medium and in the atmosphere at very high energies, to an excess of p--mesons over ,u+-mesons in cosmic rays under the earth and so on [80, 811. Some of these phenomena are experimentally observed however, the accuracy of experiments is not high and we draw only qualitative conclusion that a t very high energies. T > 10 BeV a lot of hyperons is produced. On the other hand, experimental data obtained on accelerators indicate that a t very high energies perhaps the K-meson pair production will be more likely. With the energy increase the cross section CTKK increases faster than the oyK-hyperon production cross section. This is well seen in case of x-N interaction (see Fig. 7) and, apparently, in case of N - N interactions although the accuracy of measurements is very low.

31) The assumption about a large cross section inst = u,~,) for strange particle production does not contradict experimental data that the fractions of heavy particles (i. e. including all the strange particles) a t very high energies does not exceed 20-3070 of the tctal number of produced particles (see [B]) since the strange particle production can be accompanied with the production of a large number of n-mesons. (For example, in the interaction of 16 BeV x-- mesons with protons in the reactions involving strange particles on the average 4.5 x-mesons are produced [42] ) .

Table 11 The ratio of average mumbers of K+- and x+-mesons produced in collision of protons with

nuclei (lab. sy.). Notations are the same as in Table 7.

T [BeV]

6 6 6 6

10 10 10 10 10 10

20 20 20 20 20 20 20 20 20 20 20

24 24 24 24 24

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30

33

Nucleus

Cu [82] Cu [82] Cu [82] Cu [82]

Be [47] Be [47] Be [47] Be [a71 Be [47] Cu [R3]

Be [47] Be [47] Be [-17] Be [47] Be [47] Be [a71 Be [47] Be [47] Be [47] Be [47] Be [47]

A1 [48 - 501 A1 [48--501 A1 [48-501 A1 [48-501 A1 [48-501

Be [47] Be [47] Be [47] Be [a71 Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] Be [47] A1 [47] A1 [47] A1 [47] ~i r471 AI (471 A1 [47] A1 [47]

A1 [51]

~~~~

0 [degrees]

0 30 60 90

4.75 4.75 4.75 9 9 0

4.75 4.75 4.75 4.75 2 2 2 2 9 9 9

3 6 6 6

16

4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 4.75 9 9 9

20 20 9 9 9 9

13 13 13

13.5

P [BeV/c]

0.505 0.52 0.49 0.46

3.3 4.6 7 3 5.9 4.75

4.6 5 5.5 6 7 9.2

11.2 13 3 5.9 8.9

18 5 6 8 2

3.3 3.9 4.6 5.5 6.4 6.9 7.5 9.3

11.4 13.8 15.2 8

10 11.9 1.25 2.5 3 3.9 4.9 5.9 3 6 9

2

n.g+/n,+

(1.4 5 0.4) * lo-'

(4.4 & 1.3). lo-' (3.6 f 1.4) *

(2.9 & 0.9) * 10-2

0.050 f 0.011 0.13 f 0.01 0.14 f 0.01 0.17 f 0.03 0.15 5 0.03 0.077

0.082 f 0.005 0.091 & 0.008 0.11 & 0.02 0.099 f 0.007 0.12 & 0.01 0.13 0.20 f 0.01 0.18 f 0.02 0.15 & 0.02 0.22 f 0.02 0.27 f 0.03

0.40 0.26 0.19 0.19 0.15

0.074 & 0.013 0.094 & 0.013 0.12 f 0.01 0.12 f 0.01 0.11 f 0.01 0.11 f 0.01 0.15 & 0.03 0.15 f 0.01 0.15 & 0.01 0.18 & 0.03 0.16 & 0.03 0.26 & 0.02 0.27 f 0.03 0.28 i 0.05 0.017 i 0.012 0.230 & 0.012 0.14 f 0.02 0.15 f 0.01

0.26 & 0.02 0.27 & 0.02 0.29 f 0.05 0.31 f 0.04

0.22 f 0.02

0.20 * 0.01

- d u n

GM ' .

I t

g5 - -

I --_1-

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Herausgeber: Prof. Dr. Rudolf Ritschl und Prof. Dr. Robert Rompe; Manuskripte sind zu richten an die Schrift- leitung: 11. Physikalisches Institut der Humboldt-Universitat Berlin, Berlin N 4, Hessische Str. 2. Verlag: Akademie-Verlag GmbH, Berlin W 8, Leipziger Str. 3-4, Fernruf: 220441, Telex-Nr. 011 773, Postscheckkonto: Berlin 35021. Die Zeitschrift ,,Fortschritte der Physik" erscheint monatlich; Bezugspreis dieses Heftes DM 6, - . Bestellnummer dieses Heftes: 1027/11/10. - Satz und Druck: Druckhaus ,,Maxim Gorki", Altenburg, Bez. Leipzig, Carl-von-Ossietzky-Str. 30 - 31. - Veroffentlicht unter der Liseuznummer 1324 des Presseamtes beim Vorsitzenden des Ministerrates der Deutschen Demokratischen Republik. - Alleinige Anzeigenanuahme DEWAG-Werbung, Berlin C 2, Rosenthaler StrsDe 28/31 und slle DEWAG-Betriebe in den Bezirksstadten der

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